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\newcommand{\subalgfac}{\bf{Algebra:\ Factorials}}
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\newcommand{\secbitstrings}{\bf{Counting\ Bit\ Strings}}
\newcommand{\subhs}{Counting Handshakes}
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\newcommand{\subdiscrete}{What is Discrete Mathematics?}
\newcommand{\sublearning}{Learning Discrete Mathematics}
\newcommand{\exerR}{Recap}
\newcommand{\subcountingawry}{When Counting Goes Awry}
\newcommand{\exerP}{Practice}
\newcommand{\subfactorials}{Algebra: Factorials}
\newcommand{\exerU}{Understand}
\newcommand{\subsubsetschoose}{Subsets and the Binomial Coefficients}
\newcommand{\exerE}{Explore}
\newcommand{\subcombinecount}{Combining Counting Techniques}
\newcommand{\subproofscountnosums}{Proof Format: Combinatorial Proof}
\newcommand{\subbitstrings}{Bit Strings}
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\newcommand{\subexplog}{Algebra: Exponential Notation and Logarithms}
\newcommand{\subbridges}{Crossing Bridges}
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\newcommand{\subgraphcomp}{Graph Complements}
\newcommand{\subdegseq}{Degree Sequences}
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\newcommand{\subchromatic}{Coloring Graphs}
\newcommand{\subgraphconj}{Graph Conjectures}
\newcommand{\subplanarity}{Planarity}
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\newcommand{\subnonisograph}{Nonisomorphic Graphs}
\newcommand{\subgraphclassification}{Graph Classification}
\newcommand{\subrobots}{Detour: Robots}
\newcommand{\sublockers}{Opening and Closing Lockers}
\newcommand{\subevenodd}{Even and Odd Integers}
\newcommand{\subdivides}{Divisibility}
\newcommand{\subfractions}{Algebra: Equivalent Fractions}
\newcommand{\subdivalg}{The Division Algorithm, \fn{div}, and \fn{mod}}
\newcommand{\subpolys}{Algebra: Polynomials}
\newcommand{\subpffcases}{Proof Format: Proof by Cases}
\newcommand{\subnotlast}{Not Last Game}
\newcommand{\submod}{The Mod Clock}
\newcommand{\subzn}{The Integers mod $n$}
\newcommand{\subprimes}{Primes and Composites}
\newcommand{\subprimefact}{Prime Factorization}
\newcommand{\subcountdiv}{Detour: Listing and Counting Divisors}
\newcommand{\subgcd}{Greatest Common Divisor}
\newcommand{\subea}{The Euclidean Algorithm}
\newcommand{\subcoprime}{Coprime Integers}
\newcommand{\subandor}{And and Or}
\newcommand{\subpffandor}{Proof Formats: $\land$ and $\lor$ by Cases}
\newcommand{\subequivneg}{Logical Equivalence and Negations}
\newcommand{\subpffcontra}{Proof Format: Contradiction}
\newcommand{\subsetgame}{The Game SET}
\newcommand{\subquant}{Quantifiers}
\newcommand{\subpffquants}{Proof Formats: $\forall$ and $\exists$}
\newcommand{\subcex}{Negating Quantified Statements and Counterexamples}
\newcommand{\subifthen}{Promises: Conditional Statements}
\newcommand{\subpffifthen}{Proof Format: Direct Proof of $\to$}
\newcommand{\subnegcond}{Broken Promises: Negating Conditional Statements}
\newcommand{\subpfforimplication}{Proof Formats: Proof of $\lor$ Using Implication}
\newcommand{\subconv}{The Converse and Biconditional Statements}
\newcommand{\subpffiff}{Proof Format: $\leftrightarrow$}
\newcommand{\subcp}{The Contrapositive}
\newcommand{\subpffcp}{Proof Format: $\to$ Using the Contrapositive}
\newcommand{\subequiv}{Logical Equivalence}
\newcommand{\subneg}{Simplifying Negations}
\newcommand{\subinference}{Logical Inference}
\newcommand{\subinfsetsnumbers}{Infinite sets of numbers}
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\newcommand{\subpiecewise}{Piecewise-defined Functions}
\newcommand{\subfndotgraphs}{Dot Diagrams and Graphs of Functions}
\newcommand{\subfloorceiling}{Floor and Ceiling}
\newcommand{\subnumberfn}{Number-theoretic Functions}
\newcommand{\subfngraphs}{Graph-theoretic Functions}
\newcommand{\subbitstringfunctions}{Functions Involving Bit Strings}
\newcommand{\suborderedpair}{Ordered Pairs and the Definition of Function}
\newcommand{\subpairing}{Pairings}
\newcommand{\subonetooneonto}{One-to-one and Onto}
\newcommand{\subperms}{Permutations}
\newcommand{\subinverses}{Inverse Functions}
\newcommand{\subpffunique}{Proof Format: Uniqueness}
\newcommand{\subdefnseq}{The Definition of Sequence}
\newcommand{\submodelseq}{Modeling with Explicitly-defined Sequences}
\newcommand{\subseqprimes}{Detour: Sequences Involving Primes}
\newcommand{\subelements}{Elements of a Set}
\newcommand{\subsetbuild}{Set-Builder Notation}
\newcommand{\subsetops}{Set Operations}
\newcommand{\subsubsets}{Subsets of a Set}
\newcommand{\subbsrepsubset}{Bit String Representation of Subsets}
\newcommand{\subsetsofsets}{Sets of Sets}
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\newcommand{\subdefnpartition}{The Definition of Partition}
\newcommand{\subselfconj}{Conjugate Partitions}
\newcommand{\subbulgsol}{Collecting Coins}
\newcommand{\subcartprod}{The Cartesian Product of Sets}
\newcommand{\subfncartprod}{Functions Involving Cartesian Products}
\newcommand{\subdefnrelation}{Relations and Their Representations}
\newcommand{\subrelppty}{Properties of Relations}
\newcommand{\subequivclass}{Equivalence Relations and Equivalence Classes}
\newcommand{\subcongmod}{Congruence mod $n$}
\newcommand{\subhanoi}{The Towers of Hanoi}
\newcommand{\subrecdefseq}{Recursively-defined Sequences}
\newcommand{\subntr}{Modeling with Recursively-defined Sequences}
\newcommand{\subpffmathind}{Proof Format: Mathematical Induction}
\newcommand{\subalgind}{Algebra: Evaluating $f(n-1)$}
\newcommand{\subpffindseq}{Proof Format: Special Case of Mathematical Induction for Proving an Explicit Rule for a Recursively-defined Sequence}
\newcommand{\submatpowers}{Matrix Products and Powers}
\newcommand{\subpffindmatrix}{Proof Format: Special Case of Mathematical Induction for Proving an Explicit Formula for the Power of a Matrix}
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\newcommand{\subproperbs}{Proper Bit Strings}
\newcommand{\subrecsets}{Recursively-defined Sets}
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\newcommand{\subfib}{The Fibonacci Sequence and Higher Order Recursions}
\newcommand{\submodelhigher}{Modeling with Higher Order Recursions}
\newcommand{\subfibpatterns}{Detour: Fibonacci Patterns and Proof}
\newcommand{\subpffstrongind}{Proof Format: Strong Mathematical Induction}
\newcommand{\subhowmanysq}{Counting Squares}
\newcommand{\subfactrep}{Factorial Representations}
\newcommand{\subsigmapi}{Sum and Product Notation}
\newcommand{\subbaseb}{Base $b$ Representation}
\newcommand{\subbinary}{Binary Representation}
\newcommand{\subhex}{Hexadecimal Representation}
\newcommand{\subhexforbinary}{Hex as a Shorthand for Binary}
\newcommand{\subsumconj}{Sum Conjectures}
\newcommand{\subprodconj}{Product Conjectures}
\newcommand{\subsumfib}{Detour: Fibonacci Sums}
\newcommand{\subfactorpolys}{Algebra: Factoring Polynomials}
\newcommand{\subarithtri}{The Arithmetic Triangle}
\newcommand{\subpascalpatterns}{Patterns in the Arithmetic Triangle}
\newcommand{\subbinomthm}{The Binomial Theorem}
\newcommand{\subfactorialbinom}{Explicit Formula for Binomial Coefficients}
\newcommand{\subpffsumproofsind}{Proof Format: Special Case of Mathematical Induction for Proving Sum and Product Formulas}
\newcommand{\subpffcombsums}{Proof Format: Combinatorial Proof of Sums}
\newcommand{\subspecialsum}{Detour: Special Sums}
\newcommand{\subfracalg}{Algebra: Fraction Arithmetic}
\newcommand{\subhotelinf}{Hotel Infinity}
\newcommand{\subdefndiscrete}{The Definition of Discrete}
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